When exponents are negative, we can express them using the following relationship:

$\displaystyle x^{-a}=\frac{1}{x^a}$.

In this format, $\displaystyle x$ represents the base and $\displaystyle a$ represents the exponent. A negative exponent becomes positive when it is rewritten as a reciprocal.

Therefore: 

$\displaystyle 24^{-2}=\frac{1}{24^2}=\frac{1}{576}$

When exponents are negative, we can express them using the following relationship:

$\displaystyle x^{-a}=\frac{1}{x^a}$.

In this format, $\displaystyle x$ represents the base and $\displaystyle a$ represents the exponent. A negative exponent becomes positive when it is rewritten as a reciprocal.

Therefore: 

$\displaystyle \left(\frac{1}{7}\right)^{-3}=\frac{1}{\frac{1}{7^3}}=\frac{1}{\frac{1}{343}}$

Dividing by a fraction is the same as multiplying by its reciprocal. 

$\displaystyle \frac{1}{\frac{1}{343}}=1 \times \frac{343}{1}= 343$

When exponents are negative, we can express them using the following relationship:

$\displaystyle x^{-a}=\frac{1}{x^a}$.

In this format, $\displaystyle x$ represents the base and $\displaystyle a$ represents the exponent. A negative exponent becomes positive when it is rewritten as a reciprocal.

Therefore: 

$\displaystyle \left(\frac{2}{3}\right)^{-4}=\frac{1}{(\frac{2}{3})^3}=\frac{1}{\frac{16}{81}}$

Dividing by a fraction is the same as multiplying by its reciprocal. 

$\displaystyle \frac{1}{\frac{16}{81}}=1\times\frac{81}{16}=\frac{81}{16}$

When dealing with negative exponents, we convert to fractions as such: $\displaystyle x^{-a}=\frac{1}{x^a}$ which $\displaystyle a$ is the positive exponent raising base $\displaystyle x$.

$\displaystyle 12^{-12}=\frac{1}{12^{12}}$

When dealing with negative exponents, we convert to fractions as such: $\displaystyle x^{-a}=\frac{1}{x^a}$ which $\displaystyle a$ is the positive exponent raising base $\displaystyle x$.

$\displaystyle \frac{1}{64}^{-3}=\frac{1}{\frac{1}{64^3}}=\frac{1}{\frac{1}{262144}}=262144$

When dealing with fractional exponents, we rewrite as such: $\displaystyle x^{\frac{a}{b}}=\sqrt[b]{x^a}$ which $\displaystyle b$ is the index of the radical and $\displaystyle a$ is the exponent raising base $\displaystyle x$. When dealing with negative exponents, we convert to fractions as such: $\displaystyle x^{-a}=\frac{1}{x^a}$ which $\displaystyle a$ is the positive exponent raising base $\displaystyle x$.

$\displaystyle \frac{1}{64}^{-\frac{1}{3}}=\frac{1}{\frac{1}{\sqrt[3]{64}}}=\frac{1}{\frac{1}{4}}=4$

When dealing with fractional exponents, we rewrite as such: $\displaystyle x^{\frac{a}{b}}=\sqrt[b]{x^a}$ which $\displaystyle b$ is the index of the radical and $\displaystyle a$ is the exponent raising base $\displaystyle x$. When dealing with negative exponents, we convert to fractions as such: $\displaystyle x^{-a}=\frac{1}{x^a}$ which $\displaystyle a$ is the positive exponent raising base $\displaystyle x$.

$\displaystyle \frac{1}{8}^{-\frac{2}{3}}=\frac{1}{\frac{1}{\sqrt[3]{8^2}}}=\frac{1}{\frac{1}{4}}=4$

When dealing with negative exponents, we convert to fractions as such: $\displaystyle x^{-a}=\frac{1}{x^a}$ which $\displaystyle a$ is the positive exponent raising base $\displaystyle x$.

$\displaystyle 5^{-8}=\frac{1}{5^8}$

When expressing negative exponents, we rewrite as such: 

$\displaystyle x^{-a}=\frac{1}{x^a}$ 

in which $\displaystyle a$ is the positive exponent raising base $\displaystyle x$.

$\displaystyle 21^{-2}=\frac{1}{21^2}=\frac{1}{441}$

When expressing negative exponents, we rewrite as such: 

$\displaystyle x^{-a}=\frac{1}{x^a}$ 

in which $\displaystyle a$ is the positive exponent raising base $\displaystyle x$.

$\displaystyle -4^{-4}=-\frac{1}{4^4}=-\frac{1}{256}$